Oh yeah...

Hello, all!

Second day of class for a couple of my classes, I've finished 280 and Number Theory today. Lemme tell ya, 280 went awesomely. I had a good ol' time. I mean, how hard is it to have fun when you're making up crazily false mathematical statements?

In all earnestness, I did have a lot of fun in class today, and I think we were right where we need to be, all over mathematical statements and their truth, quantifiers singly and in conjunction with one another. There was willing, active participation, there was effective group communication, there were apt, authentic, and clever examples galore (my, do I have some smart students!). There were laughs, and no tears. There was excitement. I'd be a happy man if every class I lead were to come off as well as this one did.

368 went well, too. 45 minutes of the class were spent by the students giving their presentations on the first chapter of Silverman. We had some very robust discussions on twin primes, Dirichlet's theorem and its consequences, primes of specific forms, proofs of the infinitude of primes, factorizations...we were deep enough into the discussion that we only just had enough time to spit out a few small facts about Pythagorean triples (Silverman, Chapter 2) before calling it a day.

Hijinx and hilarity outside of class, too: Karl and I spent a half hour before class looking at connections between triangle-square numbers and Pell equations, examining the limiting behavior of a curve whose infinitely many integer-valued loci give rise to triangle-square numbers.

I love these students! I'm feeling like the luckiest teacher in the world today.

Wednesday next is the first day of presentations in both classes, and I'll be fishin' for volunteers come Monday. I'm pretty sure I'll find no shortage of willing confederates: both classes are stocked with solid students chocked full of mathematical derring-do.

Now, off to Calc I in the few minutes. Dare I ask for a third wonderful class?